Tap water smells and tastes like bleach?

I understand they treat the water but I just moved to Lexington, NC ( BBQ capitol of the world! ) and the water here is clean I would ume but it's not very tasty. There is enough bleach in the water that last week a brand new grey bath towel got a bleach line in it when I threw it in the washer while the water was filling up ( was using cold water to wash and Wisk soap..no bleach was added ). Doesn't the county check it's water on a regular basis? Anybody else have this problem where they live?